Communication method, communication system, transmission device, and receiving device

ABSTRACT

A communication method of transmitting plural packets from a first communication device to a second communication device includes associating identification information items with combinations of reception results of the plural packets in the second communication device, specifying one of the identification information items based on the reception results of the plural packets in initial reception, and transmitting the one item to the first communication device; determining an encoding method and encoding the plural packets based on the determined encoding method, and retransmitting the encoded packets to the second communication device; and decoding the encoded packets based on successfully received packets and reproducing incorrectly received packets in the initial reception.

CROSS-REFERENCE TO RELATED APPLICATION

This application is a U.S. continuation application filed under 35 USC111(a) claiming benefit under 35 USC 120 and 365(c) of PCT internationalapplication PCT/JP2009/004691, filed Sep. 17, 2009, the disclosure ofwhich is hereby incorporated by reference.

FIELD

The embodiment discussed herein is related to a transmission method, atransmission system, a transmission device, and a receiving device.

BACKGROUND

There has been a known packet communication system in which upon apacket transmitted from a transmission device being not correctlyreceived by a receiving device, the receiving device does not feeds backACK (reception succeeded) but feeds back NACK (reception failed) to thetransmission device, so that the transmission device retransmits thereception-failed packet. For example, International Publication PamphletNo. WO2003/028314discloses a technique in which the transmission devicetransmits plural packets and the receiving device collectively feedsback the ACK/NACK of each of the packets.

SUMMARY

According to an aspect, a communication method of transmitting pluralpackets from a first communication device to a second communicationdevice includes associating identification information items withcombinations of reception results of the plural packets in the secondcommunication device, a number of the identification information itemsbeing less than a number of the plural packets; transmitting, by thefirst communication device, the plural packets to the secondcommunication device in initial transmission; specifying, by the secondcommunication device, a first of the identification information itemsbased on reception results of the plural packets in initial reception,and transmitting, by the second communication device, the firstidentification information item to the first communication device;determining, by the first communication device, an encoding methoddecodable by the second communication device with successfully receivedpackets in the initial reception, encoding, by the first communicationdevice, the plural packets based on the determined encoding method, andretransmitting, by the first communication device, the encoded packetsto the second communication device; and decoding, by the secondcommunication device, the encoded packets based on the successfullyreceived packets in the initial reception, and reproducing, by thesecond communication device, incorrectly received packets in the initialreception.

The object and advantage of the invention will be realized and attainedby means of the elements and combinations particularly pointed out inthe claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the invention as claimed.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a drawing illustrating a wireless communication systemaccording to an embodiment;

FIG. 2 is a drawing illustrating a generation of encoded packetsaccording to an embodiment;

FIG. 3 is a block diagram illustrating a main part of an internalconfiguration of a mobile station according to an embodiment;

FIG. 4 is a block diagram illustrating a main part of an internalconfiguration of a base station according to an embodiment;

FIG. 5 is a table illustrating corresponding relationships between errorpatterns and reception indexes;

FIG. 6 is a table illustrating corresponding relationships between thereception indexes and encoding methods adapted in the base station;

FIG. 7 is a flowchart illustrating transmission of plural packets fromthe base station to the mobile station;

FIG. 8 is a table illustrating encoding matrixes set when the number oftransmission packets is eight;

FIG. 9 is another table illustrating encoding matrixes set when thenumber of transmission packets is eight; and

FIG. 10 is a table illustrating a result of searching for the number ofthe encoding methods where feed-back information amount is minimum.

DESCRIPTION OF EMBODIMENT

In a communication system of the related art, the fed-back informationtransmitted from the receiving device receiving packets to thetransmission device refers to the information of the ACK/NACK (1 bit)for each packet. Therefore, the amount of the information to be fed backto the transmission device refers to the number of bits equal to thenumber of packets to be transmitted.

On the other hand, in a cellular communication system such as LTE (LongTerm Evolution) which has been researched by the 3GPP (3rd GenerationPartnership Project), in many cases, it may be operated undercomparatively higher packet reception error rates due to interferencenoise and multi-path fading environments; therefore, the retransmissionrate of the packets may occur with higher incidence.

Further, in the downlink of the cellular communication system, data tobe transmitted to many users (mobile stations) may be multiplexed intothe same sub frames, and the ACK/NACK information items from manymobiles stations are fed back to the base station. In the communicationsystem, the greater the information amount fed back to the base station,the more radio resources are consumed. Therefore, there is a demand toreduce the feed-back information amount described above.

Namely, it may be requested to provide a communication method, acommunication system, a transmission device, and a receiving device thatmay reduce the amount of information to be fed back from thereceiving-side transmission device to the transmitting-sidecommunication device.

In the following, as a communication system according to an embodimentof the present invention, a wireless communication system including abase station as a first communication device or a transmission deviceand a mobile station as a second communication device or a receivingdevice is described.

(1) Wireless Communication System in an Embodiment

FIG. 1 illustrates a wireless communication system according to anembodiment. As illustrated in FIG. 1, the wireless communication systemaccording to this embodiment includes a base station (BS) and a mobilestation (MS) in a service area of the wireless base station. In thisembodiment, a case is described where plural packets are transmittedfrom the base station to the mobile station.

In this wireless communication system, the packet transmission isperformed in a manner such that a predetermined number equal to two ormore of packets (i.e., plural packets) are transmitted as a unit of atransmission from the base station to the mobile station. The mobilestation determines whether each of the plural packets is receivedcorrectly (successfully) (ACK) or fails to be received correctly(incorrectly) (NACK), and feeds back the results to the base station.

Here, between the base station and the mobile station, there areprovided identification information items which are associated with(assigned to) corresponding combinations of ACK (correctly received orsuccessful reception) and NACK (incorrectly received, or receptionfailure) results of the plural packets in the mobile station. In thedescription of this embodiment, the identification information isdescribed as (called) a “reception index”. The mobile station feeds backthe reception index corresponding to the reception results of the pluralpackets to the base station.

In this wireless communication system, the base station determines anencoding method decodable by using the packets having been successfullyreceived when the packets are initially received by the secondcommunication device (i.e., the mobile station). Further, based on thedetermined encoding method, the base station encodes the plural packetsto be transmitted (to generate encoded packets). Then, the encodedpackets are transmitted to the mobile station. The mobile stationreproduces (regenerates) the packets having been incorrectly received inthe initial transmission by decoding the encoded packets using correctlyreceived packets in the initial transmission.

(2) Generation of Encoded Packets

Next, the generation of the encoded packets is described with referenceto FIG. 2. FIG. 2 illustrates the generation of the encoded packets inthis embodiment.

In FIG. 2, symbols P₁, P₂, . . . , P_(N) are assumed to be (denote) theplural packets (N packets) in the initial transmission (which refers tothe packets that are initially transmitted) from the base station to themobile station. In the initial transmission, CRC (Cyclic RedundancyCheck) codes for error detection are appended to the plural packets andFEC (Forward Error Correction) coding is further performed on the pluralpackets.

After that, the plural packets are transmitted to the mobile station. Onthe other hand, in the retransmission, the reception index (“R_IDX”) isfed back from the mobile station, and the coding method corresponding tothe reception index is selected.

Here, in a case where N packets are transmitted and M packets (fromamong the N packets) have not been correctly received, the encodingmethod in this case is expressed as in the following formula (1) byusing M×N encoding matrix G_(M,K). Here, the symbol “k” refers to asequentially assigned number to identify one of the encoding matrixesG_(M,K) which is relevant to the same number of errors “M” (error number“M”).

$\begin{matrix}{\begin{pmatrix}{R_{1}(n)} \\{R_{2}(n)} \\\vdots \\{R_{M}(n)}\end{pmatrix} = {{G_{M,k}\begin{pmatrix}{P_{1}(n)} \\{P_{2}(n)} \\\vdots \\{P_{N}(n)}\end{pmatrix}}\; {mod}\; 2}} & (1)\end{matrix}$

In formula (1), symbols P₂(n), P₂(n), . . . , and P_(N)(n) denotecorresponding nth one bit of N packets P₁, P₂, . . . , and P_(N). Then,the extracted N bits are multiplied by the M×N encoding matrix G_(M,K)to obtain N bits of R₂(n), R₂(n), . . . , and R_(N)(n). By executingthis matrix operation on each bit of N packets, M retransmission packets(encoded packets) are generated.

In each of the operations in the above formula (1), a “mod-2” operationis performed.

(3) Configurations of Base Station and Mobile Station

Next, configurations of the base station (transmission device) and themobile station (receiving device) in the wireless communication systemaccording to this embodiment are described with reference to FIGS. 3 and4.

FIG. 3 is a block diagram illustrating a main (relevant) part of aninternal configuration of the mobile station, and FIG. 4 is a blockdiagram illustrating a main part of an internal configuration of thebase station.

Configuration of Mobile Station (Receiving Device)

As illustrated in FIG. 3, the mobile station includes a receiver 31, asignal separator 32, an FEC decoder 33, a packet decoder 34, an errordetector 35, a buffer 36, a retransmission controller 37, a controlsignal generator 38, and a transmitter 39.

The signal separator 32 separates (extracts) a data signal and a controlsignal from a baseband signal acquired by the receiver 31. For example,when an OFDM (Orthogonal Frequency Division Multiplexing) communicationscheme is employed, the signal separator 32 generates a symbol sequenceof each of sub carriers based on an FFT process. Then, the data signaland the control signal inserted into a predetermined sub carrier areseparated.

The data signal and the control signal acquired by the signal separator32 are output to the FEC decoder 33. The control signal acquired by thesignal separator 32 is decoded and output to the retransmissioncontroller 37.

The FEC decoder 33 sequentially decodes the data signal by the unit ofpackets, the data signal being from the signal separator 32.

The error detector 35 detects an error by using a CRC bit appended tothe packet. As a result of the error detection, an ACK signal (receptionsucceeded) or a NACK signal (reception failed) for each of the packetsis output to the retransmission controller 37. A successfully(correctly) received packet is output to an upper layer and also storedin the buffer 36.

The packet decoder 34 decodes the encoded packet using the correctlyreceived packet in the buffer 36 under the control of the retransmissioncontroller 37, the encoded packet being transmitted from the basestation when the packet is retransmitted. Details of the decodingprocess are described below.

The retransmission controller 37 determines whether the received packetis an initially received packet (i.e., the packet when the base stationinitially transmits) or the encoded packet upon being retransmittedbased on the received control signal. Then, when determining that thereceived packet is the encoded packet, the retransmission controller 37controls the packet decoder 34.

Further, in the wireless communication system, between the mobilestation and the base station, the specific reception indexes(identification information items) are associated in advance withcorresponding combinations of the ACK (correctly received or successfulreception) and the NACK (incorrectly received, or reception failure)results of the plural packets.

Further, the retransmission controller 37 specifies the reception indexbased on the error detection results of the packets by the errordetector 35. The reception index R_IDX is multiplexed with (into) thecontrol signal by the control signal generator 38, and transmitted tothe base station by the transmitter 39.

Configuration of Base Station (Transmission Device)

As illustrated in FIG. 4, the base station includes a receiver 11, acontrol signal extractor 12, a retransmission controller 13, a buffer14, a CRC appending section 15, an FEC encoder 16, a signal multiplexer17, and transmitter 18.

The receiver 11 converts a received RF signal into a digital basebandsignal. The control signal extractor 12 extracts the control signal byperforming a predetermined signal separation process and alsodemodulation and decoding processes on the baseband signal.

The control signal includes the reception index corresponding to thereception results of the plural packets transmitted to the mobilestation. The control signal extractor 12 outputs the reception indexR_IDX to the retransmission controller 13.

The plural packets to be transmitted to the mobile station are stored inthe buffer 14 before being initially transmitted for retransmissioncontrol.

When the packets are to be retransmitted, based on the reception indexfrom the control signal extractor 12, the retransmission controller 13selects one of the plural encoding methods provided. Further, theretransmission controller 13 generates the encoded packets from theplural packets in the buffer 14 based on the selected encoding method.

In this case, the retransmission controller 13 determines the encodingmethod decodable based on the correctly received packets in the mobilestation in the initial transmission from among the plural packets to betransmitted in the buffer 14. Based on the determined encoding method,the retransmission controller 13 encodes the plural packets to betransmitted. Details of the encoding process are described below.

The CRC appending section 15 appends CRC bits to newly input packets orthe encoded packets from the retransmission controller 13 for errordetection. For error correction, the FEC encoder 16 performs encoding onthe packets to which the CRC bits are appended, the encoding for theerror correction being determined between the base station and themobile station in advance.

The signal multiplexer 17 multiplexes the data signal (packets) from theFEC encoder 16 with the control signal, to generate a baseband signal tobe transmitted. For example, when an OFDMA communication scheme isemployed, an IFFT (Inverse Fast Fourier Transform) process is performedto convert subcarriers into a time-domain signal.

The transmitter 18 upconverts the baseband signal from the signalmultiplexer 17 from the baseband frequency to a radio frequency and thelike, and emits to air (transmits the RF signal) via an antenna.

(4) Example of Packet Encoding Process and Decoding Process inRetransmission

Next, a packet encoding process and a decoding process in theretransmission of packets are specifically described by referring to anexample where the number of packets to be transmitted is four withreference to FIGS. 5 and 6.

FIG. 5 is a table illustrating relationships between plural errorpatterns (combinations of errors) assuming that the number of packets isfour and the reception indexes R_IDX correspond to the plural errorpatterns.

FIG. 6 is a table illustrating corresponding relationships between thereception indexes R_IDX and the corresponding encoding methods (encodingmatrixes) to be applied by the base station.

Further, the operations described below are bit operations (MOD-2operation).

As illustrated in FIG. 5, in response to four packets P₁, P₂, P₃, and P₄from the base station, there are sixteen possible combinations of thereception states (ACK or NACK) (i.e., error patterns 0 through 15) inthe mobile station. In the mobile station, those sixteen error patternsare associated with corresponding reception indexes in advance asillustrated in FIG. 5.

When referring to FIG. 3 again, the retransmission controller 37 of themobile station determines the reception index R_IDX by referring to thecorresponding relationship of FIG. 5 based on the reception states (ACKor NACK) of the packets, the reception states being given from the errordetector 35, and feeds back the reception index to the base station.

The corresponding relationships between the reception indexes R_IDX andthe encoding matrixes are assumed to be known to the base station inadvance. Here, when referring to FIG. 2, the retransmission controller13 of the base station (see FIG. 4) selects the encoding method(encoding matrix) for the retransmission based on the reception indexR_IDX fed back from the mobile station, and generates the encodedpackets.

Here, it is assumed that N=4 and also M×4 matrixes as the encodingmatrix G_(M,K) are set (established). Further, the number of generatedencoded packets is equal to the number of incorrectly received packet inthe mobile station.

(4-1) In a Case Where the Number of Errors (M) is “0”

In this case, as the reception index R_IDX, data “0” is fed back fromthe mobile station to the base station. By doing this, the base stationrecognizes that all packets have been correctly received, and noretransmission may have to be performed.

(4-2) In a Case Where the Number of Errors (M) is “1”

In this case, as illustrated in FIG. 5, when any one of the four packetsis incorrectly received, a value “1” is fed back from the mobile stationto the base station as the reception index R_IDX. Then, as illustratedin FIG. 6, the base station selects the encoding matrix G_(1,0)corresponding to the fed-back reception index, and generates the encodedpackets.

Specifically, the selected encoding matrix G_(1,0) is expressed in thefollowing formula (2). Therefore, when the encoded packet is given asR₁, the R₁ is given as illustrated in formula (3). In this case, onlythe single encoded packet is transmitted as the retransmission packet tothe mobile station.

Here, the symbols R₁, P₁, P₂, P₃, and P₄ denote nth bit similar toformula (1). However, in the following, it is assumed that a similarprocess is performed for each of the (n) bits. Therefore, thedescription of the factor “n” may be omitted.

G _(1,0)=(1 1 1 1)   (2)

R ₁ =P ₁ +P ₂ +P ₃ +P ₄   (3)

In the mobile station, successfully (correctly) received packets (i.e.,three packets) are known. Therefore, when the encoded packet R₁ isreceived, the three successfully received packets are cancelled(subtracted) from the encoded packet R₁. Further, as described above, inthis embodiment, the mod-2 operation is performed as the operation.Therefore, the same result may be acquired by performing an additionoperation as the cancel (subtraction) operation.

By doing this, the mobile station may correctly reproduce (decode) thepacket which has not been correctly received in the initial transmissionof the packet. For example, when assuming that the packet P₄ is theincorrectly received packet, by performing the operation based onfollowing formula (4), it may become possible to reproduce the packetP₄.

R ₁ −P ₂ −P ₃ =P ₄   (4)

The encoded packet R₁ is the sum of all the packets P₁, P₂, P₃, and P₄.Therefore, even when the incorrectly received packet is any one of thosepackets in the initial transmission, the incorrectly received packet maybe similarly reproduced by cancelling the three successfully receivedpackets from the encoded packet R₁.

Here, it should be noted is that in response to any of the four errorpatterns where the number of errors is “1”, the same value (“1”) is fedback to the base station as the reception index. Namely, there is noinformation indicating which of the four packets is the incorrectlyreceived packet among the four packets transmitted from the mobilestation to the base station.

Namely, when compared with a system where all the reception states(results) (ACK/NACK) of the packets are fed back (i.e., four bits arenecessary), it may become possible to reduce an amount of feed-backinformation (feed-back information amount) in a system according to thisembodiment.

(4-3) In a Case Where the Number of Errors (M) is “2”

In this case, a value “2” or “3” is fed back from the mobile station tothe base station as the reception index R_IDX. Further, the base stationselects an encoding matrix G_(2,0) or G_(2,1) in response to thefed-back reception index, and generates the encoded packets.

Error Pattern “5” (NACK, NACK, ACK, ACK)

In a case of an error pattern “5”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “2”, and theencoding matrix G_(2,0) is selected by the base station. In this case,two encoded packets R₁ and R₂ to be retransmitted to the mobile stationare acquired based on the following formula (5).

$\begin{matrix}{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} = {{G_{2,0}\begin{pmatrix}P_{1} \\P_{2} \\P_{3} \\P_{4}\end{pmatrix}} = {\begin{pmatrix}1 & 1 & 1 & 1 \\1 & 0 & 1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\P_{3} \\P_{4}\end{pmatrix}}}} & (5)\end{matrix}$

In the mobile station, the successfully (correctly) received packets(i.e., two packets R₃ and R₄) are known. Therefore, when the encodedpackets R₁ and R₂ are received, by cancelling (subtracting) the twosuccessfully received packets from the encoded packets R₁ and R₂, asillustrated in the formula (6), the encoded packets R₁′ and R₂′ afterthe cancel operation may be obtained.

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{3} \\P_{4}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2}\end{pmatrix}}}} & (6)\end{matrix}$

Based on the formula (6), the packet P₁ is acquired as the encodedpacket R₂′, and the packet P₂ is acquired by subtracting the packet P₁(i.e., R₂′) from the encoded packet R₁′. Namely, the matrix in the rightmember of formula (6) has an inverse matrix; therefore, P₁ and P₂ may becalculated based on R₁′ and R₂′.

Error Pattern “7” (NACK, ACK, ACK, NACK)

In a case of an error pattern “7”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “2”, and theencoding matrix G_(2,0) is selected by the base station. In this case,by cancelling the known successfully received packets (i.e., two packetsP₂ and P₃) from the two encoded packets R₁ and R₂ (see formula (5)), asillustrated in formula (7), the encoded packets R₁′ and R₂′ after thecancel operation may be acquired (calculated).

$\begin{matrix}{\begin{pmatrix}R_{1\;}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}P_{2} \\P_{3\;}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{4}\end{pmatrix}}}} & (7)\end{matrix}$

In this case similar to the case of the error pattern “5”, the packetsP₁ and P₄ may be reproduced (decoded).

Error Pattern “8” (ACK, NACK, NACK, ACK)

In a case of an error pattern “8”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “2”, and theencoding matrix G_(2,0) is selected by the base station. In this case,by cancelling the known successfully received packets (i.e., two packetsP₁ and P₄) from the two encoded packets R₁ and R₂ (see formula (5)), asillustrated in formula (8), the encoded packets R₁′ and R₂′ after thecancel operation may be acquired (calculated).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{4}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}P_{2} \\P_{3}\end{pmatrix}}}} & (8)\end{matrix}$

In this case, similar to the case of the error pattern “5”, the packetsP₂ and P₃ may be reproduced (decoded).

Error Pattern “10” (ACK, ACK, NACK, NACK)

In a case of an error pattern “10”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “2”, and theencoding matrix G_(2,0) is selected by the base station. In this case,by cancelling the known successfully received packets (i.e., two packetsP₁ and P₂) from the two encoded packets R₁ and R₂ (see formula (5)), asillustrated in formula (9), the encoded packets R₁′ and R₂′ after thecancel operation may be acquired (calculated).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2\;}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{3} \\P_{4}\end{pmatrix}}}} & (9)\end{matrix}$

In this case, similar to the case of the error pattern “5”, the packetsP₃ and P₄ may be reproduced (decoded).

Error Pattern “6” (NACK, ACK, NACK, ACK)

In a case of an error pattern “6”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “3”, and theencoding matrix G_(2,1) is selected by the base station. In this case,two encoded packets R₁ and R₂ to be retransmitted to the mobile stationare given in the following formula (10).

$\begin{matrix}{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} = {{G_{2,1}\begin{pmatrix}P_{1} \\P_{2} \\P_{3} \\P_{4}\end{pmatrix}} = {\begin{pmatrix}1 & 1 & 1 & 1 \\1 & 0 & 0 & 1\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\P_{3} \\P_{4}\end{pmatrix}}}} & (10)\end{matrix}$

In the mobile station, the successfully (correctly) received packets(two packets R₂ and R₄) are known. Therefore, when the encoded packetsR₁ and R₂ are received, by cancelling (subtracting) the two successfullyreceived packets from the encoded packets R₁ and R₂, as illustrated inthe formula (11), the encoded packets R₁′ and R₂′ after the canceloperation may be obtained. This is similar to the case of the errorpattern “5” in that the encoded packets R₁′ and R₂′ may be reproduced(decoded) based on the formula (11).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}P_{2} \\P_{4\;}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{3\;}\end{pmatrix}}}} & (11)\end{matrix}$

Next, a reason why the encoding matrix G_(2,1) selected in the case ofthe error pattern “6” is different from that selected in the cases theerror patterns “5”, “7”, “8”, and “10” (i.e., a reason why anotherreception index is selected) is described.

In the case of the error pattern “6”, when it is assumed that not theencoding matrix G_(2,1) but the encoding matrix G_(2,0) is selected,based on the formula (5), the encoded packets R₁′ and R₂′ may be givenas in the following formula (12). As is apparent from the formula (12),if the encoding matrix G_(2,0) is selected, it may not be possible touniquely determine the packets R₁ and R₂.

This occurs because the matrix in the right member of formula (12) doesnot have an inverse matrix. Therefore, in the case of the error pattern“6”, the encoding matrix G_(2,1) different from the encoding matrixG_(2,0) is set (selected) so that the matrix acquired by cancelling thesuccessfully received packets from the encoded packets has the inversematrix.

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\0 & 0\end{pmatrix}\begin{pmatrix}P_{2} \\P_{4}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\1 & 1\end{pmatrix}\begin{pmatrix}P_{1} \\P_{3}\end{pmatrix}}}} & (12)\end{matrix}$

Error Pattern “9” (ACK, NACK, ACK, NACK)

In a case of an error pattern “9”, as illustrated in FIGS. 5 and 6, thereception index R_IDX fed back to the base station is “3”, and theencoding matrix G_(2,1) is selected by the base station. In this case,by cancelling the known successfully received packets (i.e., two packetsP₁ and P₃) from the two encoded packets R₁ and R₂ (see formula (10)), asillustrated in formula (13), the encoded packets R₁′ and R₂′ after thecancel operation may be acquired (calculated). Based on the formula(13), the packets P₂ and P₄ may be reproduced (decoded).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {{\begin{pmatrix}R_{1} \\R_{2}\end{pmatrix} - {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{3}\end{pmatrix}}} = {\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}P_{2} \\P_{4}\end{pmatrix}}}} & (13)\end{matrix}$

As described above, the encoding process and the decoding process in acase where the number of errors (M) is “2” are described. In a casewhere the number of errors (M) is “2”, the 2×4 encoding matrix (a firstmatrix) is set (selected) in a manner such that a 2×2 (2: the number oferrors (M)) square matrix (a second matrix) which is decomposed(degenerated) from the 2×4 encoding matrix (the first matrix) has theinverse matrix.

The square matrix is acquired after the successfully received packetsare cancelled from the encoded packets, and is given as in the followingformula (14) or (15) when the number of errors (M) is “2”. (wheresymbols “I” and “j” denote any value from 1 to 4, respectively)

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 \\1 & 0\end{pmatrix}\begin{pmatrix}P_{i} \\P_{j}\end{pmatrix}}} & (14) \\{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 \\0 & 1\end{pmatrix}\begin{pmatrix}P_{i} \\P_{j}\end{pmatrix}}} & (15)\end{matrix}$

In this embodiment, with respect to six error patterns when the numberof errors is “2”, it may be necessary to provide (prepare) only tworeception indexes (“2” and “3”) to be fed back to the base station.Namely, when compared with a system where all the reception states(results) (ACK/NACK) of the packets are fed back (i.e., four bits arenecessary), it may become possible to reduce the feed-back informationamount in a system according to this embodiment.

(4-4) In a Case Where the Number of Errors (M) is “3”

In this case, as illustrated in FIGS. 5 and 6, a value “4” is fed backfrom the mobile station to the base station as the reception indexR_IDX. Further, the base station selects an encoding matrix G_(3,0) inresponse to the fed-back reception index, and generates three encodedpackets. Those encoded packets are given in the following formula (16).

$\begin{matrix}{\begin{pmatrix}R_{1} \\R_{2} \\R_{3}\end{pmatrix} = {\begin{pmatrix}1 & 1 & 1 & 1 \\1 & 0 & 1 & 0 \\1 & 0 & 0 & 1\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\P_{3} \\P_{4\;}\end{pmatrix}}} & (16)\end{matrix}$

Error Pattern “11” (NACK, NACK, NACK, ACK)

In a case of an error pattern “11”, by cancelling (subtracting) onesuccessfully received packet P₄ from the encoded packets transmittedfrom the base station, the encoded packets R₁′, R₂′, and R₃′ acquiredafter the cancel operation are given in the following formula (17).Further, as illustrated in the following formula (18), the determinantof the matrix in the right member of formula (17) is not “0”. Therefore,according to the formula (17), the packets P₁, P₂, and P₃ may bereproduced (decoded).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime} \\R_{3}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 & 1 \\1 & 0 & 1 \\1 & 0 & 0\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\P_{3}\end{pmatrix}}} & (17) \\{{\det \begin{pmatrix}1 & 1 & 1 \\1 & 0 & 1 \\1 & 0 & 0\end{pmatrix}} = {{\det \begin{pmatrix}0 & 1 & 0 \\0 & 0 & 1 \\1 & 0 & 0\end{pmatrix}} = 1}} & (18)\end{matrix}$

Error Pattern “12” (NACK, NACK, ACK, NACK)

In a case of an error pattern “12”, by cancelling (subtracting) onesuccessfully received packet P₃ from the encoded packets transmittedfrom the base station, the encoded packets R₁′, R₂′, and R₃′ acquiredafter the cancel operation are given in the following formula (19).Further, as illustrated in the following formula (20), the determinantof the matrix in the right member of formula (19) is not “0”. Therefore,according to the formula (19), the packets P₁, P₂, and P₄ may bereproduced (decoded).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime} \\R_{3}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 & 1 \\1 & 0 & 0 \\1 & 0 & 1\end{pmatrix}\begin{pmatrix}P_{1} \\P_{2} \\P_{4}\end{pmatrix}}} & (19) \\{{\det \begin{pmatrix}1 & 1 & 1 \\1 & 0 & 0 \\1 & 0 & 1\end{pmatrix}} = {{\det \begin{pmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{pmatrix}} = 1}} & (20)\end{matrix}$

Error pattern “13” (NACK, ACK, NACK, NACK)

In a case of an error pattern “13”, by cancelling (subtracting) onesuccessfully received packet P₂ from the encoded packets transmittedfrom the base station, the encoded packets R₁′, R₂′, and R₃′ acquiredafter the cancel operation are given in the following formula (21).Further, as illustrated in the following formula (22), the determinantof the matrix in the right member of formula (21) is not “0”. Therefore,according to the formula (21), the packets P₁, P₃, and P₄ may bereproduced (decoded).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime} \\R_{3}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 & 1 \\1 & 1 & 0 \\1 & 0 & 1\end{pmatrix}\begin{pmatrix}P_{1} \\P_{3} \\P_{4}\end{pmatrix}}} & (21) \\{{\det \begin{pmatrix}1 & 1 & 1 \\1 & 1 & 0 \\1 & 0 & 1\end{pmatrix}} = {{\det \begin{pmatrix}0 & 1 & 0 \\1 & 0 & 0 \\0 & 0 & 1\end{pmatrix}} = 1}} & (22)\end{matrix}$

Error Pattern “14” (ACK, NACK, NACK, NACK)

In a case of an error pattern “14”, by cancelling (subtracting) onesuccessfully received packet P₁ from the encoded packets transmittedfrom the base station, the encoded packets R₁′, R₂′, and R₃′ acquiredafter the cancel operation are given in the following formula (23).Further, as illustrated in the following formula (24), the determinantof the matrix in the right member of formula (23) is not “0”. Therefore,according to the formula (23), the packets P₁, P₃, and P₄ may bereproduced (decoded).

$\begin{matrix}{\begin{pmatrix}R_{1}^{\prime} \\R_{2}^{\prime} \\R_{3}^{\prime}\end{pmatrix} = {\begin{pmatrix}1 & 1 & 1 \\0 & 1 & 0 \\0 & 0 & 1\end{pmatrix}\begin{pmatrix}P_{2} \\P_{3} \\P_{4}\end{pmatrix}}} & (23) \\{{\det \begin{pmatrix}1 & 1 & 1 \\0 & 1 & 0 \\0 & 0 & 1\end{pmatrix}} = {{\det \begin{pmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1\end{pmatrix}} = 1}} & (24)\end{matrix}$

In this embodiment, with respect to four error patterns when the numberof errors is “3”, it may be necessary to provide (prepare) only onereception index (“4”) to be fed back to the base station. Namely, whencompared with a system where all the reception states (results)(ACK/NACK) of the packets are fed back (i.e., four bits are necessary),it may become possible to reduce the feed-back information amount in asystem according to this embodiment.

(4-5) In a Case Where the Number of Errors (M) is “4”

In this case, as illustrated in FIGS. 5 and 6, a value “5” is fed backfrom the mobile station to the base station as the reception indexR_IDX. Further, the base station select an encoding matrix G_(4,0) inresponse to the fed-back reception index.

The encoding matrix G_(4,0) is a 4×4 unit matrix, which is (technically)equivalent to retransmitting all the four packets P₁ through P₄.

(5) Operation When Plural Packets are Transmitted from Base Station toMobile Station

Next, an operation when plural packets are transmitted from the basestation to the mobile station is described with reference to FIG. 7.FIG. 7 is a flowchart illustrating an operation of transmitting pluralpackets from the base station to the mobile station. In the description,the elements illustrated in FIGS. 3 and 4 may be referred to.

First, N packets are transmitted from the base station to the mobilestation (in step S10). In the mobile station, the error detector 35performs error detection on each of the N packets (in step S12). Theerror detection results are output to the retransmission controller 37.

Based on the error detection results (ACK/NACK) of the packets, theretransmission controller 37 of the mobile station specifies thereception index R_IDX (step S14). Further, the error detection results(ACK/NACK) of the packets (i.e., error patterns) are associated with thecorresponding reception indexes in the base station in advance.

The mobile station transmits the specified reception index to the basestation (in step S16). In the retransmission controller 13 of the basestation, the corresponding relationship between the reception indexesand the encoding methods (encoding matrixes) are defined in advance.Therefore, the retransmission controller 13 of the base stationdetermines the encoding method based on the reception index transmittedin step S16 and performs the encoding (in step S18).

Specifically, the retransmission controller 13 multiplies the Ntransmission packets by the determined M×N (M: the number of errors)encoding matrix by the unit of bits, to generate M encoded packets. TheM encoded packets are transmitted to the mobile station (in step S20).

The mobile station receives the M encoded packets. Further, the mobilestation reproduces (replaces) the incorrectly received packets in stepS12 by decoding the encoded packets (in step S22). Specifically, thepacket decoder 34 of the mobile station reproduces the incorrectlyreceived packets by cancelling (subtracting in a bit level) thesuccessfully received packets in step S12 from the encoded packets. Thisdecoding process is described by exemplifying the case where N=4.

(6) Method of Setting Encoding Matrix in Arbitrary Number of Packets

In the above (4), with respect to the encoding process and the decodingprocess of the packets in the retransmission, a case is specificallydescribed where the number of packets to be transmitted is four.However, according to an embodiment, it may also be possible toappropriately set the encoding matrix with respect to an arbitrarynumber of packets to be transmitted. In the following, a method ofsetting an appropriate encoding matrix with respect to an arbitrarynumber of packets with a simple operation is described.

In this setting method, when assuming that the number of the packets tobe transmitted is N, the encoding matrixes corresponding to the numberof errors M (M: 1 to N-1) among N packets are calculated in thefollowing steps.

Step A

With respect to a specific number of errors M, M×N encoding matrixes aregenerated in a manner such that the elements of the matrixes aredetermined by generating random number “0” or “1”.

Step B

When assuming that M packets among N packets are incorrectly received,the number of error patterns is expressed by _(N)C_(M). With respect toeach of _(N)C_(M) error patterns, it is determined whether theincorrectly received packets may be reproduced (decoded) from (by using)the encoded packets (retransmission packets) based on the encodingmatrixes generated in step A.

Specifically, an M×M square matrix is generated, the M×M square matrixbeing a decomposed (degenerated) matrix having remaining M columnscorresponding to coefficient columns to be multiplied with theincorrectly received packets in the encoding process. When thedeterminant of the decomposed (degenerated) matrix is other than zero,it may become possible to reproduce (decode) the incorrectly receivedpackets based on the retransmission packets corresponding to the errorpattern.

Step C

Among the _(N)C_(M) error patterns, when there exist P incorrectlyreceived packets which may not be reproduced in step B, a new encodingmatrix is generated by generating the random numbers. By doing this,with respect to P incorrectly received packets, the error patterns areclassified into a group of reproducible error patterns and a group ofunreproducible error patterns.

Until all the incorrectly received packets may be reproduced for all the_(N)C_(M) error patterns, the new encoding matrix is generated bygenerating the random numbers. Namely, until all the incorrectlyreceived packets may be reproduced for all the _(N)C_(M) error patterns,the number of the encoding matrixes may be increased.

By sequentially performing the processes of the above steps A to C withrespect to the number of errors “M”, the encoding matrixes correspondingto all the numbers of errors “M” may be acquired. In accordance with thesetting method described above, in a case of N=8, the encoding matrixesas illustrated in FIGS. 8 and 9 may be acquired. FIG. 8 illustrates theencoding matrixes when the number of errors M among eight transmissionpackets is in a range from one to four, and FIG. 9 illustrates theencoding matrixes when the number of errors M among eight transmissionpackets is in a range from five to eight.

Further, it may also be possible to search for the encoding method tominimize the number of the encoding matrixes (i.e., the coding method tominimize the feed-back information amount) by performing the abovesteps, for example, 10,000,000 times by changing the random numbers.FIG. 10 illustrates a result of searching for the encoding method tominimize the feed-back information amount based on the above settingmethod when the number (N) of packets to be transmitted is in a rangefrom 1 to 11.

In FIG. 10, for example, when assuming that N=11, the number of theencoding matrixes which may be necessary in the communication methodaccording to this embodiment is 45. Further, the reception indexes areassociated with the corresponding encoding matrixes. Therefore, thefeed-back information amount (i.e., the number of bits that may expressthe reception indexes) may be six bits only.

On the other hand, as for a comparison, FIG. 10 also illustrates thefeed-back information amount in a method of the related art for each ofthe reception states (ACK/NACK) (one bit) of plural packets. In thismethod of the related art, when N=11, 11 bits may be necessary.Therefore, according to this embodiment, it may become possible togreatly reduce the feed-back information amount.

As described above, in a communication system and a communication methodaccording to this embodiment, the identification information (receptionindexes) are previously associated with the corresponding combinationsof the reception results (states) of plural packets in the mobilestation, the plural packets being transmitted from the base station. Theidentification information is fed back to the base station.

Further, by paying attention to the fact that the successfully receivedpackets in the initial transmission are known in the mobile station, thepackets to be retransmitted from the base station are encoded (as theencoded packets) based on the encoding method so that the incorrectlyreceived packets may be reproduced (decoded) based on the encodedpackets and the successfully received packets by the mobile station inthe initial transmission. The mobile station may reproduce (decode) theincorrectly received packets in the initial transmission by decoding theencoded packets using the successfully received packets in the initialtransmission.

Here, as described above, when an appropriate encoding method is set,the number of the identification information items (receptioninformation) (i.e., the number of encoding methods) may be reduced andbe less than number of packets to be transmitted; therefore thefeed-back information amount to the base station may be reduced.

According to an embodiment, a communication method of transmittingplural packets from a first communication device to a secondcommunication device includes associating identification informationitems with combinations of reception results of the plural packets inthe second communication device, a number of the identificationinformation items being less than a number of the plural packets;transmitting, by the first communication device, the plural packets tothe second communication device in initial transmission; specifying, bythe second communication device, a first of the identificationinformation items based on reception results of the plural packets ininitial reception, and transmitting, by the second communication device,the first identification information item to the first communicationdevice; determining, by the first communication device, an encodingmethod decodable by the second communication device with successfullyreceived packets in the initial reception, encoding, by the firstcommunication device, the plural packets based on the determinedencoding method, and retransmitting, by the first communication device,the encoded packets to the second communication device; and decoding, bythe second communication device, the encoded packets based on thesuccessfully received packets in the initial reception, and reproducing,by the second communication device, incorrectly received packets in theinitial reception.

According to another embodiment, a communication system includes a firstcommunication device configured to transmit plural packets and a secondcommunication device configured to receive the plural packets from thefirst communication device. Further the second communication device isconfigured to store identification information items associated withcombinations of reception results of the plural packets in the secondcommunication device, a number of the identification information itemsbeing less than a number of the plural packets. Further, the firstcommunication device includes a first transmitter configured toinitially transmit the plural packets to the second communicationdevice, a first receiver configured to receive the identificationinformation items from the second communication device, a packet encoderconfigured to determine an encoding method decodable by the secondcommunication device with successfully received packets in the initialreception, encode the plural packets based on the determined encodingmethod to generate encoded packets, and a second transmitter configuredto retransmit the encoded packets to the second communication device.Further, the second communication device includes a second receiverconfigured to initially receive the plural packets from the firstcommunication device, an information specifying unit configured tospecify a first identification information item based on the receptionresults of the plural packets, a third transmitter configured totransmit the first identification information item to the firstcommunication device, a third receiver configured to receive the encodedpackets from the first communication device, and a packet decoderconfigured to decode the encoded packets transmitted from the firstcommunication device based on the successfully received packets in theinitial reception to reproduce incorrectly received packets in theinitial reception.

According to another embodiment, a transmission device transmittingplural packets to a receiving device includes a first transmitterconfigured to initially transmit the plural packets to the receivingdevice; a first receiver configured to receive identificationinformation items from the receiving device, the identificationinformation items being associated with combinations of receptionresults of the plural packets in the receiving device; a packet encoderconfigured to determine an encoding method decodable by the receivingdevice with successfully received packets in the initial reception ofthe plural packets, encode the plural packets based on the determinedencoding method; and a second transmitter configured to retransmit theencoded packets to the receiving device.

According to another embodiment, a receiving device receiving pluralpackets from a transmission device and storing identificationinformation items associated with combinations of reception results ofthe plural packets, includes a second receiver configured to initiallyreceive the plural packets from the transmission device; an informationspecifying unit configured to specify a first of the identificationinformation items based on reception results of the plural packets;, athird transmitter configured to transmit the first identificationinformation item to the transmission device; a third receiver configuredto receive the encoded packets from the transmission device; and apacket decoder configured to decode the encoded packets transmitted fromthe transmission device based on the successfully received packets ininitial reception to reproduce incorrectly received packets in theinitial reception.

The communication method, the communication system, the transmissiondevice, and the receiving device according to an embodiment describedherein may reduce the amount of information to be fed back from thereceiving-side transmission device to the transmitting-sidecommunication device in relation to the success or failure of receivingthe plural packets.

All examples and conditional language recited herein are intended forpedagogical purposes to aid the reader in understanding the inventionand the concepts contributed by the inventors to furthering the art, andare to be construed as being without limitation to such specificallyrecited examples and conditions, nor does the organization of suchexamples in the specification relate to a showing of superiority orinferiority of the invention. Although the embodiment of the presentinvention has been described in detail, it should be understood thatvarious changes, substitutions, and alterations could be made heretowithout departing from the sprit and scope of the invention.

1. A communication method of transmitting plural packets from a firstcommunication device to a second communication device, the communicationmethod comprising: associating identification information items withcombinations of reception results of the plural packets in the secondcommunication device, a number of the identification information itemsbeing less than a number of the plural packets; transmitting, by thefirst communication device, the plural packets to the secondcommunication device in initial transmission; specifying, by the secondcommunication device, a first of the identification information itemsbased on reception results of the plural packets in initial reception,and transmitting, by the second communication device, the firstidentification information item to the first communication device;determining, by the first communication device, an encoding methoddecodable by the second communication device with successfully receivedpackets in the initial reception, encoding, by the first communicationdevice, the plural packets based on the determined encoding method, andretransmitting, by the first communication device, the encoded packetsto the second communication device; and decoding, by the secondcommunication device, the encoded packets based on the successfullyreceived packets in the initial reception, and reproducing, by thesecond communication device, incorrectly received packets in the initialreception.
 2. The communication method according to claim 1, wherein anumber of the encoded packets is the same as a number of the incorrectlyreceived packets in the initial reception in the second communicationdevice, and wherein, in the determining, the encoding, and theretransmitting, by the first communication device, the firstcommunication device generates one encoded packet based on a singlepacket of the plural packets or by adding two or more packets by thebits, and generates all the encoded packets so that each of the pluralpackets becomes any of the decoded packets or each of the plural packetsbecomes a target to be added when any of the encoded packets isgenerated.
 3. The communication method according to claim 2, wherein inthe decoding and the reproducing by the second communication device, thesecond communication device decodes the encoded packets by subtractingthe successfully received packets in the initial reception from theencoded packets by the bits.
 4. A communication system comprising: afirst communication device configured to transmit plural packets; and asecond communication device configure to receive the plural packets fromthe first communication device; wherein the second communication deviceis configured to store identification information items associated withcombinations of reception results of the plural packets in the secondcommunication device, a number of the identification information itemsbeing less than a number of the plural packets, wherein, the firstcommunication device include a first transmitter configured to initiallytransmit plural packets to the second communication device, a firstreceiver configured to receive the identification information from thesecond communication device, a packet encoder configured to determine anencoding method decodable by the second communication device withsuccessfully received packets in the initial reception, and encode theplural packets based on the determined encoding method to generateencoded packets, and a second transmitter configured to retransmit theencoded packets to the second communication device, wherein, the secondcommunication device includes a second receiver configured to initiallyreceive the plural packets from the first communication device, aninformation specifying unit configured to specify a first of theidentification information items based on the reception results of theplural packets, a third transmitter configured to transmit the firstidentification information item to the first communication device, athird receiver configured to receive the encoded packets from the firstcommunication device, and a packet decoder configured to decode theencoded packets transmitted from the first communication device based onthe successfully received packets in the initial reception to reproduceincorrectly received packets in the initial reception.
 5. Thecommunication method according to claim 4, wherein a number of theencoded packets is the same as a number of the incorrectly receivedpackets in the initial reception in the second communication device, andwherein the packet encoder is configured to generate one encoded packetbased on a single packet of the plural packets or by adding two or morepackets by the bits, and generate all the encoded packets so that eachof the plural packets becomes any of the decoded packets or each of theplural packets becomes a target to be added when any of the encodedpackets is generated.
 6. The communication method according to claim 5,wherein the packet decoder is configured to decode the encoded packetsby subtracting the successfully received packets in the initialreception from the encoded packets by the bits.
 7. The communicationmethod according to claim 5, wherein when a first matrix is expressed asan M×N matrix where a symbol N denotes a number of the plural packetsand is an integer greater than one and a symbol M denotes a number ofthe incorrectly received packets in the initial reception in the secondcommunication device from among the plural packets so that a bitsequence of M encoded packets corresponds to a bit sequence of N pluralpackets, the first matrix is set so that a second matrix expressed as anM×N matrix formed by decomposing the first matrix has an inverse matrix.8. A transmission device transmitting plural packets to a receivingdevice, comprising: a first transmitter configured to initially transmitplural packets to the receiving device; a first receiver configured toreceive identification information items from the receiving device, theidentification information items being associated with combinations ofreception results of the plural packets in the receiving device; apacket encoder configured to determine an encoding method decodable bythe receiving device with successfully received packets in initialreception of the plural packets, and encode the plural packets based onthe determined encoding method; and a second transmitter configured toretransmit the encoded packets to the receiving device.
 9. A receivingdevice receiving plural packets from a transmission device and storingidentification information items associated with combinations ofreception results of the plural packets, the receiving devicecomprising: a second receiver configured to initially receive the pluralpackets from the transmission device; an information specifying unitconfigured to specify a first of the identification information itemsbased on reception results of the plural packets; a third transmitterconfigured to transmit the first identification information item to thetransmission device; a third receiver configured to receive the encodedpackets from the transmission device; and a packet decoder configured todecode the encoded packets transmitted from the transmission devicebased on successfully received packets in initial reception to reproduceincorrectly received packets in the initial reception.